Question

Simplify: 24x⁶y⁻³ / (12x⁻⁸ y⁷)
a) 2x⁻²y⁴
b) 2x²y⁴
c) 2x⁻²y⁻⁴
d) 2x²y⁻⁴

Answer 1

To simplify the expression 24x⁶y⁻³ / (12x⁻⁸ y⁷), we divide the coefficients (24/12=2) and subtract the exponents of like bases (x⁶/x⁻⁸=x⁶+⁸=x² and y⁻³/y⁷=y⁻³-⁷=y⁻⁴) to arrive at the simplified expression 2x²y⁻⁴.

Step-by-step explanation:

The question asks us to simplify the algebraic expression 24x⁶y⁻³ / (12x⁻⁸ y⁷). To do this, we divide the coefficients and subtract the exponents of the like bases according to the laws of exponents.

First, we simplify the coefficients:

24 / 12 = 2

Next, we simplify the variables:

x⁶ / x⁻⁸ = x⁶ * x⁸ = x⁶+⁸ = x² (because a⁻⁸ = a⁸)

y⁻³ / y⁷ = y⁻³ * y⁻⁷ = y⁻³-⁷ = y⁻´

Putting it all together, we get the simplified expression:

2x²y⁻⁴